The hypotenuse of a right triangle is 17 cm long. Another side of the triangle is 7 cm longer than the third side. How do you find the unknown side lengths?
2 Answers
8 cm and 15 cm
Explanation:
Using the Pythagorean theorem we know that any right triangle with sides a, b and c the hypotenuse:
obviously the length of a side cannot be negative so the unknown sides are:
and
Explanation:
"let the third side "=x
"then the other side "=x+7larrcolor(blue)"7 cm longer"
"using "color(blue)"Pythagoras' theorem"
"square on the hypotenuse "=" sum of squares of other sides"
(x+7)^2+x^2=17^2
x^2+14x+49+x^2=289
2x^2+14x-240=0larrcolor(blue)"in standard form"
"divide through by 2"
x^2+7x-120=0
"the factors of - 120 which sum to + 7 are + 15 and - 8"
(x+15)(x-8)=0
"equate each factor to zero and solve for x"
x+15=0rArrx=-15
x-8=0rArrx=8
x>0rArrx=8
"lengths of unknown sides are"
x=8" and "x+7=8+7=15